Many different types of imaging systems are employed in modern scientific research to acquire images of small or distant objects, including extremely high-resolution electron microscopes, extremely high-resolution scanning tunneling (“STM”) and atomic-force (“AFM”) imaging instruments, and many different types of optical microscopes, telescopes, and image-generating sensors. As with most types of imaging devices, instruments, and techniques, there are many different trade-offs and balances associated with different types of microscopy. For example, transmission electron microscopy is carried out on fixed and thinly-sectioned samples, and is therefore constrained for use on essentially two-dimensional, non-living samples. Scanning-tunneling and atomic-force microscopy are non-optical techniques for obtaining high-resolution images of the surfaces of materials, but cannot be used to obtain information about the nanoscale or microscale contents of volumes of samples below surfaces. All types of microscopy are constrained, in one way or another, by resolution limitations, but optical microscopy is associated with the perhaps best-known resolution limitation referred to as the “diffraction limit,” which limits traditional visible-light optical microscopy to a resolution limit of about 200 nm
During the past 20 years, various super-resolution techniques have been developed to allow imaging of fluorophore-labeled samples, most often biological samples, by optical fluorescence-microscopy instruments at resolutions significantly below the diffraction-limited resolution for traditional optical microscopy. These techniques are based on collecting fluorescent light emitted from fluorophore-labeled samples over time. Providing that the emitting fluorophores are separated from one another by distances greater than about 200 nm, or, in other words, provided that the positions of the fluorophores in the sample would be resolvable by traditional optical microscopy, the positions of the fluorophores in a sample can be determined, in certain cases, to a resolution of below 10 nm. However, because the fluorescent-emission signal can be interpreted only when the emitting fluorophores are sparsely arranged within the sample, a generally large number of intermediate images need to be produced from different sets of sparsely arranged fluorophores in order to construct a super-resolution, final image of a fluorophore-labeled object. Thus, super-resolution images are obtained at the expense of the time needed to accumulate a relatively weak signal to produce a larger number of intermediate images. The time needed for super-resolution imaging does not favor imaging of live cells, which tend to move and change shape over the periods of time needed to collect the relatively weak signal from which super-resolution images are constructed. The long time periods needed to collect the relatively weak signal may also result in exposure of living cells to deleterious or fatal levels of electromagnetic radiation, including ultraviolet light. The time needed to acquire sufficient data for super-resolution imaging may also represent a significant experimental constraint, regardless of the type of sample that is imaged. For all these reasons, those who design and develop, manufacture, and optical microscopes continue to seek systems and methods to capture images below the diffraction limit